**Q: Solve for x:**

**|x² – 2x| = 3**

**Q: Solve the absolute value problem: |x/2 – 1/3| = 1**

**Q: Find the point(s) on the graph of the function f(x) = (x² + 6)(x – 5) where the slope of the tangent line is -2.**

**Q: Find the derivative of (x² – 5x + 2)*(x – 2/x)**

**Q: ∫sin(√x)dx**

**Q: Use polynomial long division to divide: x²/(1-3x)**

**Q: Find:**

**(a) the intervals where f(x) is increasing, the intervals where f(x) is decreasing, and **

**(b) the relative extrema of f(x) = -2x³ -9x² + 60x -8**

**Q: ∫x³/√(4 – x ^{2}) dx**

**Q: Find the average rate of change of y if x changes from 2 to 5 in the function y = x² + 2x**

**Q: ∫ x arctanx dx**

A: Integration by parts again: ∫udv = uv – ∫vdu

[Review some older examples of “integration by parts” if you are new to this!]

**Q: Consider the equation:**

**y= x²-4x+3**

** 1. Find the vertex.
2. It opens _____.
3. Find the axis of symmetry.
4. Find the minimum.
5. Find the discriminant.
6. It has ___ real solutions.
7. Find the x-intercept(s), if none, say so.
8. Find the y-intercept.**

OK. I must redeem myself in the realm of counting! Too many hasty errors on my last post for discrete math and not enough “thinking.” Don’t fall victim to this. And now to the question:

**Q: How many bit strings (reminder: a bit is either 0 or 1) of length 10 have:
**

**(a) Exactly 3 zeros?
(b) Have the same number of 0 and 1
(c) Have at least 7 zeros
(d) Have at least 3 ones?**

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